If cos alpha, cos beta, cos gamma are the dir | vedclass

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(C) We know that the identity for $\cos 2	heta$ is $\cos 2	heta = 2\cos^2 	heta - 1$. Substituting this for each term,we get: $\cos 2\alpha + \cos

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$-1$

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(C) We know that the identity for $\cos 2	heta$ is $\cos 2	heta = 2\cos^2 	heta - 1$. Substituting this for each term,we get: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)$. This simplifies to: $2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$. Since $\cos \alpha, \cos \beta, \cos \gamma$ are the direction cosines of a vector $\vec{a}$,we know that $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Substituting this value into the expression: $2(1) - 3 = 2 - 3 = -1$.

If $\cos \alpha, \cos \beta, \cos \gamma$ are the direction cosines of a vector $\vec{a}$,then $\cos 2 \alpha + \cos 2 \beta + \cos 2 \gamma$ is equal to

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